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Post Hoc Tests: Least Significant Difference

The normal practice for much work using analysis of variance (ANOVA) employs the use of omnibus tests to determine whether or not differences exist in the marginal means for variables (main effects) as well as whether or not combinations of levels of variables produce unique effects (interaction among variables). The omnibus test indicates that there probably exists at least one significant difference between means. In the case where a variable has only two levels, any significant difference indicates that comparing the means for the two levels (e.g., gender as measured by biological male or female) are different. In such cases, the need for a post hoc, or after-the-fact test of differences does not exist. However, suppose that there are three levels of a variable (high, ...

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